V(t) = \[Vocos(wt + \phi)\]

and to convert between real time and phasor notation use:

V(t) = Re {Ve\[^{jwt}\]}

But in every example (and by every example I mean the only 2 in the book ) the \[e^{jwt}\] is omitted from the answer. Is this because you assume the \[jw\] or \[\theta\] is constant somehow? I was just confused because it seems like you "lose" information about the signal if you don't explicitly tag on the \[e^{jwt}\] on every signal you put into the phasor domain.

Maybe it'll make more sense if someone can explain how to represent the following signals as phasors:

a) \[cos(wt)\] (= \[e^{jwt}\] ? since \[\phi\] is zero? )

b) \[3cos((120\pi t) - \pi /2)\] ( = \[6e^{-j\pi / 2}e^{j120\pi t} \]or just\[ 6e^{-j\pi / 2} \]?)